Signal processing apparatus and method, recording medium and program

ABSTRACT

A signal processing apparatus and method is disclosed by which signal components of different musical intervals of an audio signal can be obtained with a small amount of arithmetic operation. A re-sampling section re-samples an audio signal inputted thereto with a sampling frequency equal to a power-of two times a frequency at a boundary of an octave. An octave dividing block divides the audio signals outputted from the re-sampling section into audio signals of octaves and outputs the resulting audio signals to respective band-pass filter banks. Each of the band-pass filter banks includes 12 band-pass filters and extracts and outputs audio signals of 12 musical intervals from the audio signals of one octave. The invention can be applied to a signal processing apparatus which analyzes, for example, signal components of musical intervals of an audio signal.

BACKGROUND OF THE INVENTION

This invention relates to a signal processing apparatus and method, arecording medium and a program, and more particularly to a signalprocessing apparatus and method, a recording medium and a program bywhich signal components of different musical intervals of an audiosignal can be obtained.

Various musical interval estimation methods have been proposed whereinsignal components obtained by sampling a digital audio (music) signalwith a predetermined sampling frequency are classified into signalcomponents of different musical intervals (scales) such as, for example,C, C#, D, D#, E, F, F#, G, G#, A, A# and B (which correspond to do, do#,re, re#, mi, fa, fa#, so, so#, la, la# and ti, respectively). Suchestimation of musical intervals of an audio signal is utilized, forexample, for automatic music transcription, music analysis (melodyanalysis) and so forth.

The twelve musical intervals of C, C#, D, D#, E, F, F#, G, G#, A, A# andB construct one octave, and the frequencies of musical intervals of oneoctave are equal to twice those of musical intervals lower by one octavethan the musical intervals. In other words, musical intervals aredistributed logarithmically (exponentially) with respect to thefrequency. For example, if the frequency (center frequency) of themusical interval of A (la) of a certain octave is 440 Hz, then thefrequency of the musical interval of A (la) higher by one octave is 880Hz which is equal to twice 440 Hz. Meanwhile, for example, thedifference in frequency (center frequency) between C4 (do) and C#4 (do#)which are adjacent each other is approximately 6 Hz in the octave 2 onthe low frequency region side, but is approximately 123 Hz in the octave6 on the high frequency region side.

Also the frequency bands (bandwidths) of the musical intervals of acertain octave are twice those of the musical intervals lower by oneoctave.

Incidentally, as an estimation method of musical intervals of an audiosignal (signal components of musical intervals included in the audiosignal), for example, a method which uses short-time Fourier transformand a method which uses wavelet conversion are available.

The short-time Fourier transform analyzes frequency components atfrequencies spaced at equal distances from each other while musicalintervals are distributed logarithmically with respect to the frequencyas described above. Therefore, according to a musical intervalestimation method which uses the short-time Fourier transform, there isa tendency that the frequency resolution is insufficient on the lowfrequency region side but is excessive on the high frequency regionside.

In particular, in the short-time Fourier transform, not only highmusical intervals, that is, musical intervals having broad frequencybands, but also low musical intervals, that is, musical intervals havingnarrow frequency band, are analyzed with frequencies spaced at equaldistances from each other. Therefore, the frequency resolution of highmusical intervals is relatively high while the frequency resolution oflow musical intervals is relatively low.

On the other hand, if it is tried to assure a sufficient frequencyresolution on the low frequency region side, then the time resolutionbecomes excessive on the low frequency region side. On the contrary, ifit is tried to assure a sufficient and necessary frequency resolution onthe high frequency region side, then the time resolution becomesinsufficient on the high frequency region side.

Further, when the short-time Fourier transform is used to estimatemusical intervals, it is necessary to take it consideration that musicalintervals are distributed logarithmically with respect to the frequencyto apply a non-linear process for a result of analysis of frequencycomponents at equal distances obtained by the Fourier transform. Due tothe non-linear process, the musical interval estimation method whichuses the short-time Fourier transform has a problem that the process iscomplicated.

Thus, according to a musical interval estimation method which uses thewavelet conversion, it is considered that musical intervals can beestimated with an ideal time-base resolution and frequency resolution byusing a basis function which can extract a 1/12 octave (one musicalinterval).

As a further musical interval estimation method for an audio signal, amethod is available wherein a BPF (Band Pass Filter) bank which includesone BPF for each musical interval of each octave is used to obtainsignal components of the musical intervals of the octaves as disclosed,for example, in Japanese Patent Publication No. Sho 61-26067. However,where a BPF bank is used, it is necessary to design the BPFs so that,for example, an appropriate time resolution and frequency resolution maybe obtained for each octave.

However, where the method which uses the wavelet conversion or a BPFbank is applied, for example, to analysis of musical intervals for theoverall audio frequencies, a very great amount of arithmetic operationis required, and therefore, the methods are poor in practical use.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a signal processingapparatus and method, a recording medium and a program by which signalcomponents of different musical intervals of an audio signal can beobtained with a small amount of arithmetic operation.

In order to attain the object described above, according to an aspect ofthe present invention, there is provided a signal processing apparatusfor processing an audio signal, comprising an octave dividing sectionfor dividing an input signal into high frequency components on a highfrequency band side and low frequency components on a low frequency bandside and down sampling the high frequency components and the lowfrequency components individually to divide the audio signal into aplurality of signals of different octaves, and a filter section forfiltering the signals of the different octaves to extract a plurality ofsignals of different musical intervals.

According to another aspect of the present invention, there is provideda signal processing method for a signal processing apparatus whichprocesses an audio signal, comprising an octave dividing step ofdividing an input signal into high frequency components on a highfrequency band side and low frequency components on a low frequency bandside and down sampling the high frequency components and the lowfrequency components individually to divide the audio signal into aplurality of signals of different octaves, and a filter step offiltering the signals of the different octaves to extract a plurality ofsignals of different musical intervals.

According to a further aspect of the present invention, there isprovided a recording medium on or in which a computer-readable programfor causing a computer to execute processing of an audio signal isrecorded, the program comprising an octave dividing step of dividing aninput signal into high frequency components on a high frequency bandside and low frequency components on a low frequency band side and downsampling the high frequency components and the low frequency componentsindividually to divide the audio signal into a plurality of signals ofdifferent octaves, and a filter step of filtering the signals of thedifferent octaves to extract a plurality of signals of different musicalintervals.

According to a still further aspect of the present invention, there isprovided a program for causing a computer to execute processing of anaudio signal, comprising an octave dividing step of dividing an inputsignal into high frequency components on a high frequency band side andlow frequency components on a low frequency band side and down samplingthe high frequency components and the low frequency componentsindividually to divide the audio signal into a plurality of signals ofdifferent octaves, and a filter step of filtering the signals of thedifferent octaves to extract a plurality of signals of different musicalintervals.

According to the signal processing apparatus and method, recordingmedium and program, an input signal is divided into high frequencycomponents on the high frequency band side and low frequency componentson the low frequency band side, and the high and low frequencycomponents are individually down sampled to divide the audio signal intoa plurality of signals of different octaves. Further, the signal of eachof the octaves is filtered to extract a plurality of signals ofdifferent musical intervals.

With the signal processing apparatus and method, recording medium andprogram, signal components of individual musical intervals of an audiosignal can be obtained with a small amount of arithmetic operation.

The above and other objects, features and advantages of the presentinvention will become apparent from the following description and theappended claims, taken in conjunction with the accompanying drawings inwhich like parts or elements denoted by like reference symbols.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a view illustrating musical intervals and frequencies of anaudio signal;

FIG. 2 is a block diagram showing an example of a configuration of asignal processing apparatus to which the present invention is applied;

FIG. 3 is a block diagram showing an example of a detailed configurationof an octave dividing block shown in FIG. 2;

FIG. 4 is a block diagram showing an example of a detailed configurationof an octave dividing section shown in FIG. 3;

FIGS. 5 and 6 are views illustrating a concept of a result of a processof an audio signal;

FIG. 7 is a block diagram showing an example of a detailed configurationof a BPF bank shown in FIG. 2;

FIGS. 8A and 8B, and 9 are views illustrating a concept of a process ofthe BPF bank of FIG. 7;

FIG. 10 is a flow chart illustrating a musical interval analysis processof the signal processing apparatus of FIG. 2;

FIG. 11 is a flow chart illustrating an octave dividing processillustrated in FIG. 10;

FIG. 12 is a flow chart illustrating an octave 8 extraction processillustrated in FIG. 11;

FIG. 13 is a flow chart illustrating a musical interval extractionprocess illustrated in FIG. 10;

FIG. 14 is a view illustrating the number of times of arithmeticoperation according to a related-art technique;

FIGS. 15 and 16 are views illustrating the number of times of arithmeticoperation according to a technique to which the present invention isapplied; and

FIG. 17 is a block diagram showing an example of a configuration of acomputer to which the present invention is applied.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Before the best mode for carrying out the present invention is describedin detail, a corresponding relationship between several features recitedin the accompanying claims and particular elements of the preferredembodiment described below is described. It is to be noted, however,that, even if some mode for carrying out the invention which is recitedin the specification is not described in the description of thecorresponding relationship below, this does not signify that the modefor carrying out the invention is out of the scope or spirit of thepresent invention. On the contrary, even if some mode for carrying outthe invention is described as being within the scope or spirit of thepresent invention in the description of the corresponding relationshipbelow, this does not signify that the mode is not within the spirit orscope of some other invention than the present invention.

Further, the following description does not signify all of the inventiondisclosed in the present specification. In other words, the followingdescription does not deny the presence of an invention which isdisclosed in the specification but is not recited in the claims of thepresent application, that is, the description does not deny the presenceof an invention which may be filed for patent in a divisional patentapplication or may be additionally included into the present patentapplication as a result of later amendment.

According to claim 1 of the present invention, there is provided asignal processing apparatus (for example, a signal processing apparatus11 of FIG. 2) for processing an audio signal, comprising an octavedividing section (for example, an octave dividing block 22 of FIG. 2)for dividing an input signal into high frequency components on a highfrequency band side and low frequency components on a low frequency bandside and down sampling the high frequency components and the lowfrequency components individually to divide the audio signal into aplurality of signals of different octaves, and a filter section (forexample, BPFBs 23 ₁ to 23 ₈ of FIG. 2) for filtering the signals of thedifferent octaves to extract a plurality of signals of different musicalintervals.

The signal processing apparatus according to claim 2 may furthercomprise a re-sampling section (for example, a re-sampling section 21 ofFIG. 2) for re-sampling the audio signal.

In the signal processing apparatus according to claim 4, the filtersection may include 12 band-pass filters (for example, BPFs 101 ₁ to 101₁₂ of FIG. 7) having pass bands for audio signals of frequency ranges of12 musical intervals.

According to claim 5 of the present invention, there is provided asignal processing method for a signal processing apparatus whichprocesses an audio signal, comprising an octave dividing step (forexample, a process at step S2 of FIG. 10) of dividing an input signalinto high frequency components on a high frequency band side and lowfrequency components on a low frequency band side and down sampling thehigh frequency components and the low frequency components individuallyto divide the audio signal into a plurality of signals of differentoctaves, and a filter step (for example, a process at step S3 of FIG.10) of filtering the signals of the different octaves to extract aplurality of signals of different musical intervals.

Also a program of a recording medium and a program according to claims 6and 7 of the present invention individually comprise particular stepssimilar to those of the signal processing method according to claim 5.

In the following, a preferred embodiment of the present invention isdescribed with reference to the accompanying drawings.

First, a relationship between musical intervals and frequencies isdescribed with reference to FIG. 1.

In FIG. 1, it can be seen that frequencies within a range from 63.55 Hzto 16,267.4 Hz are divided into 8 octaves from the octave 1 to octave 8(hereinafter referred to also as O1 to O8). Each octave includes 12musical intervals (sounds) of C (do), C#, D (re), D#, E (mi), F (fa),F#, G (so), G#, A (la), A# and B (ti) in an ascending order of thefrequency. The 12 musical intervals of C, C#, D, D#, E, F, F#, G, G#, A,A# and B of the octave 1 (O1) are hereinafter referred to as C1, C#1,D1, D#1, E1, F1, F#1, G1, G#1, A1, A#1 and B1, respectively, and the 12musical intervals of C, C#, D, D#, E, F, F#, G, G#, A, A# and B of theoctave 2 (O2) are hereinafter referred to as C2, C#2, D2, D#2, E2, F2,F#2, G2, G#2, A2, A#2 and B2, respectively. This similarly applies tothe octaves 3 (O3) to 8 (O8).

In FIG. 1, the frequencies of the 12 musical intervals of each of theoctaves 1 to 8 are determined in the following manner, for example,using A3 (la) of the octave 3 as a reference sound having a frequency(center frequency) of 440 Hz.

Since the musical intervals are distributed logarithmically with respectto the frequency as described hereinabove, where one octave isclassified into 12 sounds, the ratio in frequency (ratio in centerfrequency) between adjacent musical intervals is 1:

(the twelfth root of 2). Also the ratio in frequency region betweenadjacent musical intervals is 1:

(the twelfth root of 2).

For example, the frequency (center frequency) of the musical intervalA#3 higher by one musical interval than the musical interval of A3 ofthe octave 3 is 466.2 Hz which is equal to

times the frequency 440.0 of A3, and the frequency of the musicalinterval B3 higher by one musical interval than the musical interval ofA#3 is 493.9 Hz which is equal to

times that of A#3. For example, the frequencies of the musical intervalsof A3 of the octave 3 to C5 of the octave 5 illustrated in FIG. 1 aredetermined similarly.

Since a set of every 12 musical intervals from a musical interval of C(do) to another musical interval of B (ti) is defined as one octave, thefrequency range of the octave 4 is from the lowest frequency of thefrequency range of C4 to the highest frequency of the frequency range ofB4 (lowest frequency of the frequency range of the octave 5), that is,from 508.6 Hz to 1,016.7 Hz. It is to be noted that the term from fa[Hz] to fb [Hz] regarding the frequency represents “equal to or higherthan fa [Hz] but lower than fb [Hz]”.

Further, the center frequency and the frequency range of C5 of theoctave 5 which is higher by one octave than C4 of the octave 4 are1,046.5 Hz and 1,016.7 Hz to 1,077.2 Hz which are equal to twice those,respectively. Also with regard to the other octaves of the octave 1 tooctave 8, the frequency range of the octave and the center frequency andthe frequency range of each of the 12 musical intervals in the octaveare determined similarly. The value of the frequency at each of theboundaries between octaves such as 508.4 Hz and 1,016.7 Hz in FIG. 1 ishereinafter referred to as frequency (boundary frequency) on a boundaryof an octave or between octaves.

It is to be noted that, in FIG. 1, illustration of the centerfrequencies and the frequency ranges of the 12 musical intervals of theoctaves 1 to 8 is omitted except the octave 4 and some musical intervalsof the octaves 3 and 5.

FIG. 2 shows an example of a configuration of a signal processingapparatus 11 to which the present invention is applied.

The signal processing apparatus 11 includes a re-sampling section 21, anoctave dividing block 22, and BPFBs 23 ₁ to 23 ₈.

An audio signal (input signal) inputted to the signal processingapparatus 11 is an audio signal produced by sampling with apredetermined sampling rate. Here, it is assumed that the input signalis, for example a signal reproduced from a CD (Compact Disk), and thesampling frequency of the input signal is 44.1 kHz.

The re-sampling section 21 re-samples the inputted audio signal with adesired sampling frequency different from the sampling frequency of 44.1kHz of the audio signal. Then, the re-sampling section 21 outputs theaudio signal re-sampled with the desired sampling frequency to theoctave dividing block 22.

The sampling frequency of the re-sampling performed by the re-samplingsection 21 is determined in the following manner.

The octave dividing block 22 at the stage succeeding the re-samplingsection 21 divides an input signal inputted thereto into two componentsof high frequency components and low frequency components as hereinafterdescribed. Then, the octave dividing block 22 down samples the high andlow frequency components individually with a sampling frequency equal toone half the sampling frequency of the input signal. Then, a result ofthe sampling of the high frequency components is extracted as a signalof one octave.

On the other hand, a result of the down sampling of the low frequencycomponents is further divided into two frequency components of highfrequency components and low frequency components and down sampled to ½.Then, a result of the down sampling of the high frequency components isextracted as a signal of an octave lower by the octave extracted in thepreceding cycle. Thereafter, the octave dividing block 22 extracts aplurality of signals of different octaves similarly.

Since the octave dividing block 22 repeats frequency band division intohigh frequency components and low frequency components and ½ downsampling to extract signals of octaves in this manner, a value obtainedby dividing the sampling frequency of the audio signal inputted to theoctave dividing block 22 by 2^(n) (n=1, 2, . . . ) makes a boundaryfrequency of an octave. If it is assumed that an audio signal inputtedis not re-sampled with a desired sampling frequency by the re-samplingsection 21 and consequently is inputted to the octave dividing block 22while it keeps the sampling frequency of 44.1 kHz, then since the audiosignal is frequency band divided by the octave dividing block 22, asignal of a frequency range of 44.1 kHz/2 to (44.1 kHz/2)/2 is obtained.In this instance, the lowest frequency and the highest frequency of thehigh frequency components do not coincide with any of the boundaryfrequencies of the octaves 1 to 8 illustrated in FIG. 1. As a result,the low frequency band side or the high frequency band side of the highfrequency components exhibits lack of some frequency components of asignal of musical intervals of a desired octave or exhibits containmentof some frequency components of a signal of musical intervals of anotheroctave adjacent a desired octave. Consequently, a process of extractingsignals of different musical intervals is complicated.

Therefore, the re-sampling section 21 re-samples the original audiosignal with a sampling frequency equal to a power-of two times aboundary frequency so that the lowest frequency and the highestfrequency of high frequency components obtained for each repetition offrequency band division and down sampling of the signal may coincidewith the highest frequency and the lowest frequency of certain octavesat the octave dividing block 22 at the stage succeeding the re-samplingsection 21.

In the present embodiment, the re-sampling section 21 re-samples theaudio signal, for example, with a sampling frequency of 2⁵ times of1,016.7 Hz which is the boundary frequency between the octaves 4 and 5,that is, with the sampling frequency of 32,534.7 Hz. It is to be notedthat what value should be adopted as a sampling frequency of a power-oftwo times a boundary frequency of an octave is determined, for example,depending upon a musical interval of what height an octave to beextracted should include.

The octave dividing block 22 divides the audio signal outputted from there-sampling section 21 into signal components (audio signals) of theoctaves 1 to 8. Then, the octave dividing block 22 outputs the audiosignals of the octaves i (i=integer from 1 to 8) to the BPFBs 23 _(i).In particular, the octave dividing block 22 outputs the audio signals ofthe octave 1 to the BPFB 23 ₁, outputs the audio signals of the octave 2to the BPFB 23 ₂ and similarly outputs the audio signals of the octaves3 to 8 to the BPFBs 23 ₃ to 23 ₈, respectively.

Each of the BPFBs 23 _(i) has 12 BPFs (Band Pass Filters) having passbands for audio signals of frequency ranges of the 12 musical intervalsof C, C#, D, D#, E, F, F#, G, G#, A, A# and B. Thus, each of the BPFBs23 _(i) filters audio signals of the octave i inputted thereto from theoctave dividing block 22 to extract 12 audio signals of differentmusical intervals.

In other words, the BPFB 23 _(i) extracts audio signals of 12 musicalintervals of the octave i by means of the 12 BPFs. For example, the BPFB23 ₁ extracts signal components of the musical intervals of C1, C#1, D1,D#1, E1, F1, F#1, G1, G#1, A1, A#l and B1 as seen in FIG. 2. Similarly,for example, the BPFB 23 ₈ extracts signal components of the musicalintervals of C8, C#8, D8, D#8, E8, F8, F#8, G8, G#8, A8, A#8 and B8.

In the signal processing apparatus 11 of FIG. 2 having such aconfiguration as described above, the re-sampling section 21 re-samplesan audio signal, and the octave dividing block 22 divides the audiosignal into signals of the octaves 1 to 8. Further, the BPFBs 23 ₁ to 23₈ individually extract and output signals of 12 musical intervals fromthe signals of the octaves 1 to 8.

FIG. 3 shows in block diagram an example of a detailed configuration ofthe octave dividing block 22 shown in FIG. 2.

Referring to FIG. 3, the octave dividing block 22 includes seven octavedividing sections 51 ₁ to 51 ₇. The seven octave dividing sections 51 ₁to 51 ₇ perform basically similar processing.

Each of the octave dividing sections 51 _(j) (j=1, 2, . . . , 6, 7)divides the audio signal inputted thereto into high frequency componentson the high frequency side and low frequency components on the lowfrequency side. Further, each of the octave dividing sections 51 _(j)performs down sampling of reducing the sample number of each of audiosignals of high frequency components (hereinafter referred to as highfrequency band audio signals) and audio signals of low frequencycomponents (hereinafter referred to as low frequency band audio signal)to ½.

Further, each of the octave dividing sections 51 _(j) outputs highfrequency band audio signals after the down sampling as audio signals ofthe octave [9−j] to the BPFB 23 _(9−j) (FIG. 2). Further, the octavedividing section 51 _(j) outputs low frequency band audio signals afterthe down sampling to the octave dividing section 51 _(j+1). However,where j=7, the octave dividing section 51 ₇ outputs low frequency bandaudio signals after the down sampling as audio signals of the octave 1to the BPFB 23 ₁ (FIG. 2).

Now, processing of the octave dividing section 51 _(j) is described.

An audio signal re-sampled with the sampling frequency of 32,534.7 Hzand inputted from the re-sampling section 21 is inputted to the octavedividing section 51 ₁. The octave dividing section 51 ₁ frequency banddivides the inputted audio signal so as to divide the frequency band ofthe same into two frequency bands. In particular, where the samplingfrequency of the audio signal inputted to the octave dividing section 51₁ is represented by f_(s), the octave dividing section 51 ₁ divides theaudio signal into high frequency components on the high frequency sidefrom f_(s)/2 to (f_(s)/2)/2 and low frequency components on the lowfrequency side from 0 to (f_(s)/2)/2. Further, the octave dividingsection 51 ₁ down samples the audio signals of the high frequencycomponents and the audio signals of the low frequency componentsobtained by the frequency division to ½, for example, by sampling outthe samples.

Then, the octave dividing section 51 ₁ outputs the audio signals of thehigh frequency components after the down sampling as audio signals of anoctave to the BPFB 23 ⁸⁽⁼⁹⁻¹⁾ (FIG. 2). Further, the octave dividingsection 51 ₁ outputs the audio signals of the low frequency componentsafter the down sampling to the octave dividing section 51 ₂₍₌₁₊₁₎.

Also the octave dividing sections 51 ₂ to 51 ₇ perform similarprocessing to that of the octave dividing section 51 ₁ for audio signalssupplied thereto from the octave dividing sections 51 ₁ to 51 ₆ at thepreceding stage, respectively. However, the octave dividing section 51 ₇further frequency band divides audio signals of the low frequencycomponents after the down sampling and down samples resulting audiosignals of high frequency components to ½. Then, the octave dividingsection 51 ₇ outputs audio signals of high frequency components afterthe down sampling to the BPFB 23 ₁ (FIG. 2).

The octave dividing block 22 performs such processing as describedabove, and consequently, audio signals of the frequency range of theoctave 8 (O8) from within the original audio signal, that is, of thefrequency range from 8,133.7 Hz to 16,267.4 Hz, are outputted from theoctave dividing section 51 ₁ to the BPFB 23 ₈ (FIG. 2).

Similarly, audio signals of the octave 7 (O7) of the frequency range of4,066.8 Hz to 8,133.7 Hz are outputted to the BPFB 23 ₇; audio signalsof the octave 6 (O6) of the frequency range of 2,033.4 Hz to 4,066.8 Hzare outputted to the BPFB 23 ₆; audio signals of the octave 5 (O5) ofthe frequency range of 1,016.7 Hz to 2,033.4 Hz are outputted to theBPFB 23 ₅; audio signals of the octave 4 (O4) of the frequency range of508.4 Hz to 1,016.7 Hz are outputted to the BPFB 23 ₄; audio signals ofthe octave 3 (O3) of the frequency range of 254.2 Hz to 508.4 Hz areoutputted to the BPFB 23 ₃; audio signals of the octave 2 (O2) of thefrequency range of 127.1 Hz to 254.2 Hz are outputted to the BPFB 23 ₂;and audio signals of the octave 1 (O1) of the frequency range of 63.55Hz to 127.1 Hz are outputted to the BPFB 23 ₁.

In short, the octave dividing block 22 repeats division of the inputsignal into high frequency components on the high frequency side and lowfrequency components on the low frequency side and down sampling of thehigh frequency components and the low frequency components thereby todivide the audio signal into signals of eight octaves.

Accordingly, the octave dividing block 22 can extract 8 octaves of theoctaves 1 to 8 corresponding to a logarithmic distribution offrequencies of musical intervals. In other words, the octave dividingblock 22 can extract audio signals of each octave with a time-baseresolution and a frequency resolution which increase in proportion tothe amount of information which the octave has.

FIG. 4 shows an example of a detailed configuration of the octavedividing sections 51 ₁ to 51 ₇ of FIG. 3.

Each of the octave dividing sections 51 _(j) (j=1, 2, . . . , 6, 7)includes an HPF (High Pass Filter) 71 _(j), a DS (Down Sampling) section72 _(j), an LPF (Low Pass Filter) 73 _(j) and another DS section 74_(j). It is to be noted, however, that the octave dividing section 51 ₇further includes an HPF 75 and a DS section 76.

Audio signals are inputted to the HPF 71 _(j) and the LPF 73 _(j) of theoctave dividing section 51 _(j) from the preceding stage to the octavedividing section 51 _(j). The HPF 71 _(j) and the LPF 73 _(j) frequencyband divide the audio signals inputted thereto.

In particular, the HPF 71 _(j) extracts, from among the audio signalsinputted thereto, high frequency band audio signals having frequencieshigher than a frequency equal to ½ the frequency band of the inputtedaudio signals, and outputs the extracted high frequency band audiosignals to the DS section 72 _(j). Meanwhile, the LPF 73 _(j) extracts,from among the audio signals inputted thereto, low frequency band audiosignals having frequencies lower than the frequency equal to ½ thefrequency band of the inputted audio signals, and outputs the extractedlow frequency band audio signals to the DS section 74 _(j).

Each of the DS sections 72 _(j) and 74 _(j) down samples the audiosignals inputted from the HPF 71 _(j) or LPF 73 _(j) with a samplingfrequency equal to one half the sampling frequency of the inputted audiosignals.

The DS section 72 _(j) outputs the audio signals after the down samplingas audio signals of the octave [9−j] to the BPFB 23 _(9−j) (FIG. 2). TheDS section 74 _(j) outputs the audio signals after the down sampling tothe HPF 71 _(j+1) and the LPF 73 _(j+1) of the octave dividing section51 _(j+1) at the succeeding stage. It is to be noted, however, that theDS section 74 ₇ in the octave dividing section 51 ₇ outputs audiosignals after the down sampling to the HPF 75. Then, the HPF 75extracts, from among the audio signals after the down sampling from theDS section 74 ₇, high frequency band audio signals having frequencieshigher than a frequency equal to one half the frequency band of theaudio signals and outputs the extracted high frequency band audiosignals to the DS section 76. The DS section 76 down samples the audiosignals from the HPF 75 with a sampling frequency equal to one half thesampling frequency of the audio signals and outputs the down sampledaudio signals as audio signals of the octave 1 to the BPFB 23 ₁ (FIG.2).

FIGS. 5 and 6 illustrate a concept of a result of processing of audiosignals by the HPFs 71 _(j) and the DS sections 72 _(j) (j=1, 2, . . . ,6, 7) shown in FIG. 4.

Each of the HPFs 71 _(j) extracts (passes therethrough) audio signals ofhigh frequency components on the high frequency band side from betweenfrequency components on the high frequency band side and frequencycomponents on the low frequency band side from among audio signalsinputted thereto as audio signals of one octave. The audio signals ofthe one octave are audio signals of the octave [9−j] and includes the 12musical intervals of C, C#, D, D#, E, F, F#, G, G#, A, A# and B as seenin FIG. 5.

Then, the audio signals of the high frequency components of FIG. 5having passed through the HPF 71 _(j) are down sampled with a samplefrequency of ½ by the DS section 72 _(j).

FIG. 6 illustrates audio signals for one octave after the down samplingby the DS section 72 _(j). The audio signals of the high frequencycomponents of FIG. 5 appear reciprocally on the low frequency side bydown sampling by the DS section 72 _(j). Accordingly, in the audiosignals of the high frequency components after the down sampling, thelist of signal components of musical intervals on the frequency axis isreverse to the list of C, C#, D, D#, E, F, F#, G, G#, A, A# and B beforethe down sampling as seen in FIG. 6. In other words, the high-low listof the musical interval is reverse.

Now, an example of a detailed configuration of the BPFBs 23 ₁ to 23 ₈ isdescribed. The BPFBs 23 ₁ to 23 ₈ have a similar configuration, and FIG.7 shows an example of a detailed configuration only of the BPFB 23 _(1.)

The BPFB 23 ₁ includes 12 BPFs 101 ₁ to 101 ₁₂ having pass bandscorresponding to frequency ranges of the 12 musical intervals of C1,C#1, D1, D#1, E1, F1, F#1, G1, G#1, A1, A#l and B1, respectively.

In particular, the BPF 101 ₁ extracts, from audio signals of the octave1 inputted from the octave dividing block 22 (FIG. 3), the audio signalof the musical interval of C1 and outputs the audio signal.

The BPF 101 ₂ extracts, from the audio signals of the octave 1, theaudio signal of the musical interval of C#l and outputs the audiosignal. Similarly, the BPFs 101 ₃ to 101 ₁₂ extract the audio signals ofthe musical intervals of D1, D#1, E1, F1, F#1, G1, G#1, A1, A#1 and B1and outputs the extracted audio signals, respectively.

Processing of the BPFB 23 ₁ of FIG. 7 is described with reference toFIGS. 8 and 9. FIGS. 8 and 9 illustrate a concept of the processing ofthe BPFB 23 ₁.

FIG. 8A illustrates frequency components of audio signals of the octave1 supplied from the octave dividing block 22 to the BPFB 23 ₁. Asdescribed hereinabove with reference to FIG. 6, the audio signals of theoctave 1 outputted from the octave dividing block 22 have a list ofmusical intervals on the frequency axis which is reverse in the high-lowdirection.

Therefore, the BPFs 101 ₁ to 101 ₁₂ of FIG. 7 have such filtercharacteristics as illustrated in FIG. 8B. In particular, the BPFs 101 ₁to 101 ₁₂ of FIG. 7 are formed as filters which pass therethrough thefrequency components of the frequency ranges of C1, C#1, D1, D#1, E1,F1, F#1, G1, G#1, A1, A#1 and B1 whose list is reverse in the high-lowdirection, respectively.

In particular, the BPF 101 ₁ extracts, from among the audio signals ofthe octave 1 outputted from the octave dividing block 22, a signal ofthe highest frequency band to obtain a frequency component of C1 of thelowest musical interval. The BPF 101 ₁ extracts, from among the audiosignals of the octave 1 outputted from the octave dividing block 22, asignal of the second highest frequency band to obtain a frequencycomponent of C#1 of the second lowest musical interval. Similarly, theBPF 101 ₁ extracts, from among the audio signals of the octave 1outputted from the octave dividing block 22, signals of the successivelylower frequency bands until a signal of the lowest frequency band isextracted to obtain a frequency component of B1 of the highest musicalinterval.

In FIG. 9, the BPFs 101 ₃ to 101 ₁₂ having filter characteristics shownin FIG. 8B are illustrated in a corresponding relationship to the blockdiagram of FIG. 7.

It is to be noted that the path bands of the BPFBs 23 _(k) (k=1, 2, . .. , 12) corresponding to the BPFBs 23 ₁ to 23 ₈ are different from eachother. In particular, the BPFs 101 _(k) of the BPFB 23 _(i) whichprocesses audio signals of the octave i and the BPFs 101 _(k) of theBPFB 23 _(i+1) which processes audio signals of the octave [i+1] havepath bands which are different by twice. In short, the path band of eachof the BPFs 101 _(k) of the BPFB 23 _(i+1) is twice that of acorresponding one of the BPFs 101 _(k) of the BPFB 23 _(i).

Now, a musical interval analysis process of the signal processingapparatus 11 of FIG. 2 is described with reference to a flow chart ofFIG. 10. The musical interval analysis process of FIG. 10 is started,for example, when an audio signal is inputted to the signal processingapparatus 11 of FIG. 2.

First at step S1, the re-sampling section 21 re-samples the audio signalinputted thereto with a desired sampling frequency (in the presentembodiment, 32,534.7 Hz). Then the re-sampling section 21 outputs theaudio signal re-sampled with the desired sampling frequency to theoctave dividing block 22, and thereafter, the processing advances tostep S2.

At step S2, the octave dividing block 22 divides the audio signaloutputted from the re-sampling section 21 into audio signals of theoctaves 1 to 8. Then, the octave dividing block 22 outputs the audiosignals of the octaves i (i=inter of 1 to 8) to the BPFBs 23 _(i).Thereafter, the processing advances to step S3.

At step S3, each of the BPFBs 23 _(i) extracts, from the audio signal ofthe octave i inputted from the octave dividing block 22, the audiosignals of the 12 musical intervals by means of 12 BPFs (Band PassFilters) which have pass bands for audio signals within the frequencyranges of the 12 musical intervals of C, C#, D, D#, E, F, F#, G, G#, A,A# and B. Thereafter, the processing is ended.

Now, the octave dividing process of the octave dividing block 22 of FIG.3 is described with reference to a flow chart of FIG. 11. It is to benoted that the octave dividing process corresponds to the process atstep S2 of FIG. 10.

First at step S21, the octave dividing section 51 ₁ divides audiosignals inputted thereto from the re-sampling section 21 into audiosignals of a high frequency region and audio signals of a low frequencyregion. Further, the octave dividing section 51 ₁ performs down samplingof reducing the sample numbers of the audio signals in the highfrequency region and the audio signals in the low frequency regionindividually to one half. Further, at step S21, the octave dividingsection 51 ₁ outputs the audio signals in the high frequency regionafter the down sampling as audio signals of the octave 8 (O8) to theBPFB 23 ₁ (FIG. 2) and outputs the audio signals in the low frequencyregion after the down sampling to the octave dividing section 51 ₂.Thereafter, the processing advances to step S22.

At each of steps S22 to S26, the octave dividing section 51 _(j) (j=2, .. . , 6) divides audio signals inputted thereto (audio signals of lowfrequency components obtained by frequency division by the octavedividing section 51 _(j−1) at the preceding stage) into audio signals ina high frequency region and audio signals in a low frequency region.Further, the octave dividing section 51 _(j) performs down sampling ofreducing the sample numbers of the audio signals in the high frequencyregion and the audio signals in the low frequency region individually toone half. Further, the octave dividing section 51 _(j) outputs the audiosignals in the high frequency region after the down sampling as audiosignals of the octave [9−j] to the BPFB 23 _(9−j) (FIG. 2) and outputsthe audio signals in the low frequency region after the down sampling tothe octave dividing section 51 _(j+) 1.

After step S26, the processing advances to step S27, at which the octavedividing section 51 ₇ divides audio signals inputted thereto from theoctave dividing section 51 ₆ into audio signals in a high frequencyregion and audio signals in a low frequency region. Further, the octavedividing section 51 ₇ performs down sampling of reducing the samplenumbers of the audio signals in the high frequency region and the audiosignals in the low frequency region individually to one half. Further,the octave dividing section 51 ₇ outputs the audio signals in the highfrequency region after the down sampling as audio signals of the octave2 to the BPFB 23 ₂ (FIG. 2). Thereafter, the processing advance to stepS28.

At step S28, the octave dividing section 51 ₇ further frequency banddivides the audio signals of low frequency components after the downsampling and down samples audio signals of high frequency componentsobtained by the frequency division to one half. Further, the octavedividing section 51 ₇ outputs the audio signals of the high frequencycomponents after the down sampling as audio signals of the octave 1 tothe BPFB 23 ₁ (FIG. 2). Thereafter, the processing is ended.

Now, the extraction process of the octave 8 by the octave dividingsection 51 ₁ of FIG. 4 is described with reference to a flow chart ofFIG. 12. It is to be noted that the extraction process of the octave 8corresponds to the process at step S21 of FIG. 11.

First at step S41, the HPF 71 ₁ extracts, from among audio signalsinputted thereto from the re-sampling section 21, audio signals in ahigh frequency region higher than one half the frequency band of theinputted audio signals, and outputs the extracted audio signals to theDS section 72 ₁. Thereafter, the processing advances to step S42.

At step S42, the DS section 72 ₁ down samples the audio signals inputtedthereto from the HPF 71 ₁ with a sampling frequency equal to one halfthe sampling frequency of the inputted audio signals, and outputs theaudio signals after the down sampling as audio signals of the octave 8to the BPFB 23 ₈. Thereafter, the processing advances to step S43.

At step S43, the LPF 73 ₁ extracts, from among the audio signalsinputted thereto from the re-sampling section 21, audio signals in a lowfrequency region lower than one half of the frequency band of theinputted audio signals, and outputs the extracted audio signals to theDS section 74 ₁. Thereafter, the processing advances to step S44.

At step S44, the DS section 74 ₁ outputs the audio signals after thedown sampling to the HPF 71 ₂ and the LPF 73 ₂ of the octave dividingsection 51 ₂. Thereafter, the processing is ended.

Processes similar to the processes at steps S41 to S44 are executed alsoby the octave dividing sections 51 ₂ to 51 ₇. However, in the octavedividing section 51 ₇, the DS section 74 ₇ outputs audio signals afterdown sampling to the HPF 75 as described hereinabove. Thus, the HPF 75extracts, from among the audio signals after the down sampling from theDS section 74 ₇, audio signals in a high frequency band higher than onehalf the frequency band of the audio signals, and outputs the extractedaudio signals to the DS section 76. The DS section 76 samples the audiosignals inputted thereto from the HPF 75 with a sampling frequency equalto one half the sampling frequency of the audio signals, and outputs thedown sampled audio signals as audio signals of the octave 1 to the BPFB23 ₁ (FIG. 2).

Now, the musical interval extraction process of the BPFB 23 ₁ of FIG. 7is described with reference to a flow chart of FIG. 13. While themusical interval extraction process corresponds to the musical intervalextraction process executed by the BPFB 23 ₁ from within the musicalinterval extraction process at step S3 of FIG. 10, also the other BPFBs23 ₂ to 23 ₈ execute processes similar to the musical interval detectionprocess of FIG. 13 for the individual octaves 2 to 8, respectively.

First at step S61, the BPF 101 ₁ extracts an audio signal of the musicalinterval of C1. In particular, the BPF 101 ₁ extracts, from among audiosignals of the octave 1 inputted from the octave dividing block 22 (FIG.2), the audio signal of the musical interval of C1. Thereafter, theprocessing advances to step S62.

At steps S62 to S72, the BPFs 101 ₂ to 101 ₁₂ extract audio signals ofthe musical intervals of C#1, D1, D#1, E1, F1, F#1, G1, G#1, A1, A#1 andB1, respectively, similarly as in the extraction of the audio signal ofthe musical interval of C1 at step S61. Thereafter, the processing isended.

It is to be noted that the processes at steps S61 to S72 may be executedin an arbitrary order other than the order described above withreference to FIG. 13 or may otherwise be executed parallelly(concurrently).

In this manner, the signal processing apparatus 11 can divide an audiosignal inputted thereto into 8 octaves of the octaves 1 to 8 and furtherextract, for each of the octaves 1 to 8, audio signals of the 12 musicalintervals of C, C#, D, D#, E, F, F#, G, G#, A, A# and B. In other words,the signal processing apparatus 11 can obtain signal components ofdifferent musical intervals of an audio signal inputted thereto in atime series.

Since the signals outputted from the signal processing apparatus 11 aresignals of the 12 musical intervals of C, C#, D, D#, E, F, F#, G, G#, A,A# and B of each of the octaves 1 to 8, an apparatus which receives theoutputs of the signal processing apparatus 11 can use the musicalinterval signals (musical interval information) as they are in anapplication such as automatic music transcription, music analysis(melody analysis) and so forth.

The number of times of arithmetic operation executed for one sample ofan original audio signal to extract audio signals of the 12 musicalintervals of the totaling eight octaves of the octaves 1 to 8 differsamong different techniques for extraction of such audio signals. Now,the number of arithmetic operations performed by a simple technique(hereinafter referred to as related-art technique) which depends upon aBPF bank wherein one BPF is used for each one musical interval toextract audio signals of the individual musical intervals and the numberof times arithmetic operation performed by another technique(hereinafter referred to as present technique) which uses the signalprocessing apparatus 11 of FIG. 1 to extract audio signals of theindividual musical intervals are compared with each other. It is to benoted that the number of arithmetic operations is counted such that aset of one addition operation and one multiplication operation iscounted as one.

FIG. 14 illustrates the number of times of arithmetic operations by therelated-art technique.

According to the related-art technique, since down sampling is notperformed, the down sampling number DS is 1 in all octaves of theoctaves 1 to 8. Here, the down sampling number DS represents to whatfraction the sample number of audio signals of an object of processingis reduced with respect to the sample number of an original audiosignal. Thus, according to the related-art technique, since an originalaudio signal becomes an object of processing of BPFs for extractingsignals of the musical intervals of the octaves, the down samplingnumber DS is always equal to 1.

Further, in the related-art technique, it is assumed that, for the BPFsfor extracting audio signals of the musical intervals of the octave 8,an FIR (Finite Impulse Response) filter of 128 taps is used. Now, if itis tried to achieve a frequency resolution similar to that of the octave8 with regard to each of the octaves 1 to 7, then there is the necessityto set the number of taps of the BPFs to twice that of the BPFs forextracting the musical intervals of the of the octave 8 as the musicalintervals become lower by one octave from those of the octave 8.Accordingly, if the number of taps of each of the BPFs for extractingthe musical intervals of the octave is 128 as described above, then thenumber Tap of taps for the octaves 1 to 7 is 16,384, 8,192, 4,096,2,048, 1,024, 512 and 256, respectively.

Under such a condition as described above, the number of times ofarithmetic operation of multiplication and addition performed per onesample of the original audio signal in order to obtain the musicalintervals of each octave can be calculated by Tap÷DS×12. Accordingly,the number of times of arithmetic operation for individual ones of theoctaves 1 to 8 (that is, the number of times of arithmetic operation perone sample of original audio signals necessary to determine each of the12 musical intervals of each octave) is 196,608, 98,304, 49,152, 24,576,12,288, 6,144, 3072 and 1,536, respectively. Therefore, according to therelated-art technique, the number of times of arithmetic operation perone sample of original audio signals necessary to determine each of the12 musical intervals of each of the 8 octaves of the octaves 1 to 8 isthe sum of the values and 391,680.

FIG. 15 illustrates the numbers of times of arithmetic operations of theHPFs 71 _(j) and the LPFs 73 _(j) of the octave dividing sections 51_(j) (j=1, 2, . . . , 6, 7) of the present technique. It is to be notedhere that the number of times of arithmetic operation of the LPF 73 ₇includes also the number of times of arithmetic operation of the HPF 75.

In the present technique, in order to achieve an extraction accuracy(performance) of musical intervals equal to that of the related-arttechnique of FIG. 14, each of the HPFs 71 _(j) and the LPFs 73 _(j)requires a number of taps approximately equal to 256. Therefore, in FIG.15, the tap numbers Tap of the HPFs 71 _(j) and the LPFs 73 _(j) areboth represented as 256.

Further, as described hereinabove with reference to FIG. 4, since eachof the octave dividing sections 51 _(j) performs ½ down sampling, thedown sampling number DS of the octave 8 having the highest frequencyband is 2, and the down sampling number DS is doubled together withevery decrease of the frequency band by one octave. Accordingly, thedown sampling numbers DS of the octaves 1 to 8 are 256, 128, 64, 32, 16,8, 4 and 2, respectively.

The number of times of arithmetic operation of multiplication andaddition performed per one sample of an original audio signal by both ofthe HPFs 71 _(j) and the LPFs 73 _(j) is determined by Tap÷DS×2.Accordingly, the numbers of times of arithmetic operation ofmultiplication and addition performed per one sample of original audiosignals by both of the HPFs 71 _(j) and the LPFs 73 _(j) for the octaves1 to 8 are 2, 4, 8, 16, 32, 64, 128 and 256, respectively, as seen inFIG. 15. Accordingly, the number of times of arithmetic operation ofmultiplication and addition performed per one sample of an originalaudio signal for frequency band division by the octave dividing block 22is the sum of the numbers of times of arithmetic operation for theoctaves and 510.

FIG. 16 illustrates the numbers of times of arithmetic operation by theBPFBs 23 ₁ to 23 ₈ of the present technique.

The down sampling numbers DS for the octaves 1 to 8 are 256, 128, 64,32, 16, 8, 4 and 2 similarly as in FIG. 15. Meanwhile, the tap numbersTap of the BPFBs 23 ₁ to 23 ₈ for extracting the musical intervals ofthe octaves 1 to 8 are all 64.

Accordingly, the numbers of times of arithmetic operation by the BPFBs23 ₁ to 23 ₈ for the octaves 1 to 8 of the present technique (numbers oftimes of arithmetic operation per one sample of original audio signalsnecessary to determine the 12 individual musical intervals of an octave)are calculated by Tap÷DS×12 as seen in FIG. 16 and are 3, 6, 12, 24, 48,96, 192 and 384, respectively. Accordingly, according to the presenttechnique, the number of times of arithmetic operation per one sample oforiginal audio signals necessary to determine the 12 musical intervalsof the eight octaves of the octaves 1 to 8 is the sum of them and 765.

From the foregoing, the number of times of arithmetic operationaccording to the present technique is 1,275 which is the sum total of510 which is the number of times of arithmetic operation by the HPFs 71_(j) and the LPFs 73 _(j) of the octave dividing block 22 illustrated inFIGS. 15 and 765 which is the number of times of arithmetic operation bythe BPFBs 23 ₁ to 23 ₈ illustrated in FIG. 16.

The number of times of arithmetic operation of the present technique(the number of times of arithmetic operation performed for an input ofone sample of an original signal) is 1,275 and is extremely smaller than391,680 which is the number of times of arithmetic operation of therelated-art technique illustrated in FIG. 14. In particular, byemploying down sampling, signals of individual musical intervals can beextracted from an original audio signal through a smaller amount ofarithmetic operation than that of the related-art technique. In otherwords, according to the present technique, the amount of arithmeticoperation (performance) required for extraction of signals of musicalintervals can be reduced significantly when compared with therelated-art technique.

While the series of processes described hereinabove with reference toFIGS. 10 to 13 can be executed by hardware for exclusive use, it mayotherwise be executed by software. Where the series of processesdescribed above are executed by software, for example, the series ofprocesses can be implemented by causing a program to be executed by sucha (personal) computer as shown in FIG. 17.

Referring to FIG. 17, a CPU (central processing unit) 301 executesvarious processes in accordance with a program stored in a ROM (ReadOnly Memory) 302 or a program loaded from a storage section 308 into aRAM (Random Access Memory) 303. Also data necessary for the CPU 301 toexecute the processes are suitably stored into the RAM 303.

The CPU 301, ROM 302 and RAM 303 are connected to one another by a bus304. Also an input/output interface 305 is connected to the bus 304.

An inputting section 306 including a keyboard, a mouse and so forth, anoutputting section 307 including a display unit which may be a CRT(Cathode Ray Tube) or an LCD (Liquid Crystal Display) unit, a speakerand so forth, a storage section 308 formed from a hard disk or the like,and a communication section 309 including a modem, a terminal adapterand so forth are connected to the input/output interface 305. Thecommunication section 309 performs a communication process through anetwork such as the Internet.

Further, as occasion demands, a drive 310 is connected to theinput/output interface 305. A magnetic disk 321, an optical disk 322, amagneto-optical disk 323, a semiconductor memory 324 or the like issuitably loaded into the drive 310, and a computer program read from theloaded medium is installed into the storage section 308 as occasiondemands.

While, in the embodiment described above, a set of every 12 musicalintervals from the musical interval of C (do) to the musical interval ofB (ti) is determined as one octave, one octave may be defined by a setof different musical intervals. For example, also where the 12 musicalintervals from the musical interval of F (fa) to the musical interval ofE (mi) is determined as one set, since the frequencies exhibit alogarithmic distribution, they can be regarded as one octave.

Also the sampling frequency in re-sampling of the re-sampling section 21need not be a power-of two times a boundary frequency of an octave. Inparticular, the sampling frequency in re-sampling of the re-samplingsection 21 may be, for example, a power-of two times a frequency on theboundary between adjacent musical intervals.

Further, if the sampling frequency of an original audio signal is apower-of two times a boundary frequency of an octave or a frequency of aboundary between musical intervals, then the signal processing apparatus11 can be configured without provision of the re-sampling section 21.

It is to be noted that, in the present specification, the steps whichare described in the flow charts may be but need not necessarily beprocessed in a time series in the order as described, and includeprocesses which are executed in parallel or individually without beingprocessed in a time series.

1. A signal processing apparatus for processing an audio signal,comprising: an octave dividing section for dividing an input signal intohigh frequency components on a high frequency band side and lowfrequency components on a low frequency band side and down sampling thehigh frequency components and the low frequency components individuallyto divide the audio signal into a plurality of signals of differentoctaves; and a filter section for filtering the signals of the differentoctaves to extract a plurality of signals of different musicalintervals.
 2. A signal processing apparatus according to claim 1,further comprising a re-sampling section for re-sampling the audiosignal.
 3. A signal processing apparatus according to claim 2, whereinsaid octave dividing section divides the input signal into the highfrequency components and the low frequency components by which afrequency band of the input signal is divided equally into two frequencybands and performs down sampling of decreasing the number of samples toone half individually for the high frequency components and the lowfrequency components, and said re-sampling section re-samples the audiosignal with a sampling frequency equal to a power-of two times afrequency at a boundary of each of the octaves.
 4. A signal processingapparatus according to claim 1, wherein said filter section includes 12band-pass filters having pass bands for audio signals of frequencyranges of 12 musical intervals.
 5. A signal processing method for asignal processing apparatus which processes an audio signal, comprising:dividing an input signal into high frequency components on a highfrequency band side and low frequency components on a low frequency bandside and down sampling the high frequency components and the lowfrequency components individually to divide the audio signal into aplurality of signals of different octaves; and filtering the signals ofthe different octaves to extract a plurality of signals of differentmusical intervals.
 6. A computer readable recording medium includingcomputer executable instructions, wherein the instructions, whenexecuted by a processor, cause the processor to perform a methodcomprising: dividing an input signal into high frequency components on ahigh frequency band side and low frequency components on a low frequencyband side and down sampling the high frequency components and the lowfrequency components individually to divide the audio signal into aplurality of signals of different octaves; and filtering the signals ofthe different octaves to extract a plurality of signals of differentmusical intervals.
 7. A signal processing apparatus for processing anaudio signal, comprising: an octave dividing unit configured to dividean input signal into high frequency components on a high frequency bandside and low frequency components on a low frequency band side and todown sample the high frequency components and the low frequencycomponents individually to divide the audio signal into a plurality ofsignals of different octaves; and a filter configured to filter thesignals of the different octaves to extract a plurality of signals ofdifferent musical intervals.
 8. A signal processing apparatus accordingto claim 7, further comprising a re-sampling unit configured tore-sample the audio signal.
 9. A signal processing apparatus accordingto claim 8, wherein said octave dividing unit is configured to dividethe input signal into the high frequency components and the lowfrequency components by which a frequency band of the input signal isdivided equally into two frequency bands and to perform down sampling bydecreasing the number of samples to one half individually for the highfrequency components and the low frequency components, and saidre-sampling unit is configured to re-sample the audio signal with asampling frequency equal to a power-of two times a frequency at aboundary of each of the octaves.
 10. A signal processing apparatusaccording to claim 7, wherein said filter includes 12 band-pass filtershaving pass bands for audio signals of frequency ranges of 12 musicalintervals.